On an ordinary night of football at Camp Nou earlier this month, a baby-faced sprite resembling a ball boy who ran onto the pitch put everything—past and future—into perspective.

It has been six years since the day when Barcelona delivered a 4-0 beatdown of Levante, a game where for 60 minutes all 11 Barça players had their football roots in La Masia, the now-iconic squat stone house that sits in the shadow of the Camp Nou. That extraordinary night built expectation never again to be realized, because you don’t win the lottery twice, even as supporters of FC Barcelona have come to believe that world-class players should emerge from the club’s academy like wee footballing versions of Suzuki violin automatons.

The FC Barcelona first team is a rough place to be, even harder to get to. The club’s academy makes professionals, even if it doesn’t very often make professionals fit to hang with Messi. But in that recent match against Cultural...